During the late 18th century, France faced a major economic crisis due to Louis XVI's intervention in the American Revolution along with a regressive system of taxation. Not only were the royal coffers depleted, but the poor were already being plagued by two decades of poor harvests, drought, cattle disease and skyrocketing bread prices. These reasons had created a stir among peasants and the urban poor. Further, Parisians grew panicked as rumours of an impending military coup began circulating.
"The Storming of the Bastille" refers to a popular insurgency that culminated on 14th July when rioters stormed the Bastille fortress in an attempt to secure gunpowder and weapons. Now, many celebrate this event as a national holiday, as the start of the French Revolution. In France, "le quatorze juillet" (14 July) is the National Day, usually called 'Bastille Day' in English.
Here is a video on the French Revolution.